Subgroups — C₅×#19425 #11942145

Order 1280.

660 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3207	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3109	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1703	C₂	1	2	yes	maximal, complemented
6	C₅×#1697	C₂	1	2	yes	maximal, complemented
7	C₅×#1687	C₂	1	2	yes	maximal, complemented
8	C₅×#1685	C₂	1	2	yes	maximal, complemented
9	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₅×#493	C₂²	1	1	yes	characteristic, complemented
16	C₅×#492	C₂²	1	1	yes	characteristic, complemented
17	C₅×#487	C₂²	1	1	yes	characteristic, complemented
18	C₅×#486	C₂²	1	1	yes	characteristic, complemented
19	C₅×#481	—	2	1	no	—
20	C₅×#480	—	2	1	no	—
21	C₅×#476	C₂²	1	2	yes	—
22	C₅×#474	C₂²	1	2	yes	—
23	C₅×#463	—	2	2	no	—
24	C₅×#459	C₂²	1	2	yes	—
25	C₅×#459	C₂²	1	2	yes	—
26	C₅×#449	—	2	2	no	—
27	C₅×#447	—	2	1	no	—
28	C₅×#447	—	2	1	no	—
29	C₅×#442	—	2	2	no	—
30	C₄×C₅×D₈	—	2	2	no	—
31	C₅×#436	—	2	2	no	—
32	C₅×#436	C₂²	1	2	yes	—
33	C₅×#436	C₂²	1	2	yes	—
34	C₅×#432	C₂²	1	1	yes	characteristic
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₅×#407	—	2	2	no	—
39	C₅×#335	C₂²	1	2	yes	complemented
40	C₅×#334	C₂²	1	2	yes	complemented
41	C₅×#333	C₂²	1	2	yes	complemented
42	C₅×#332	C₂²	1	2	yes	complemented
43	C₅×#331	C₂²	1	2	yes	complemented
44	C₅×#331	C₂²	1	2	yes	complemented
45	#19425	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	1	no	—
47	C₂×C₅×#41	—	2	1	no	—
48	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	—	2	1	no	—
50	C₂×C₅×SD₁₆	—	2	2	no	—
51	C₂×C₅×D₈	—	2	2	no	—
52	C₂×C₅×D₈	—	2	2	no	—
53	C₂×C₅×D₈	—	2	2	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₅×#127	C₂³	1	1	yes	characteristic
59	C₅×#127	C₂³	1	1	yes	characteristic
60	C₅×#124	—	2	1	no	—
61	C₅×#124	—	2	1	no	—
62	C₅×#121	—	2	1	no	—
63	C₅×#121	—	2	1	no	—
64	C₅×#121	—	2	1	no	—
65	C₅×#121	—	2	1	no	—
66	C₄×C₅×D₄	—	2	1	no	—
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	D₄	1	2	yes	—
73	C₄×C₅×D₄	C₂³	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	2	2	no	—
78	C₅×#106	—	2	2	no	—
79	C₅×C₄⋊C₈	D₄	1	2	yes	—
80	C₅×C₄⋊C₈	C₂³	1	2	yes	—
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×C₄⋊C₈	C₂³	1	2	yes	—
83	C₅×#103	—	2	2	no	—
84	C₅×#102	—	2	2	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×#102	—	2	2	no	—
89	C₅×C₂²⋊C₈	—	2	1	no	—
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×C₂²⋊C₈	—	2	1	no	—
92	C₅×C₂²⋊C₈	—	2	2	no	—
93	C₅×C₂²⋊C₈	—	2	2	no	—
94	C₅×C₂²⋊C₈	D₄	1	2	yes	—
95	C₅×#97	—	2	1	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	#3207	C₂×C₅	1	1	yes	characteristic, complemented
101	#3109	C₂×C₅	1	1	yes	characteristic, complemented
102	#3100	C₂×C₅	1	1	yes	characteristic, complemented
103	#2975	C₂×C₅	1	1	yes	characteristic, complemented
104	#1703	C₂×C₅	1	2	yes	complemented
105	#1697	C₂×C₅	1	2	yes	complemented
106	#1687	C₂×C₅	1	2	yes	complemented
107	#1685	C₂×C₅	1	2	yes	complemented
108	#1572	C₂×C₅	1	1	yes	characteristic, complemented
109	#1553	C₂×C₅	1	1	yes	characteristic, complemented
110	#1543	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂⁴×C₅	—	2	1	no	—
112	C₅×#41	—	8	2	no	—
113	C₅×#41	—	8	2	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	—	4	2	no	—
124	C₂×C₅×D₄	—	4	1	no	—
125	C₂×C₅×D₄	—	4	1	no	—
126	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	4	1	no	—
131	C₂²×C₄×C₅	—	4	1	no	—
132	C₂²×C₄×C₅	—	8	2	no	—
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	#41	1	1	yes	characteristic
136	C₅×SD₁₆	—	8	2	no	—
137	C₅×D₈	—	4	4	no	—
138	C₅×D₈	—	4	4	no	—
139	C₅×D₈	—	8	2	no	—
140	C₅×M₁₆	—	8	2	no	—
141	C₅×M₁₆	—	8	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₅×C₂²⋊C₄	—	2	2	no	—
154	C₅×C₂²⋊C₄	—	2	2	no	—
155	C₅×C₂²⋊C₄	—	4	1	no	—
156	C₅×C₂²⋊C₄	—	4	1	no	—
157	C₅×C₂²⋊C₄	—	4	1	no	—
158	C₅×C₂²⋊C₄	—	4	1	no	—
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₅	#41	1	1	yes	characteristic
162	C₄²×C₅	C₂⁴	1	1	yes	characteristic
163	#532	C₂²×C₅	1	1	yes	characteristic
164	#532	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
166	#493	C₂²×C₅	1	1	yes	characteristic, complemented
167	#492	C₂²×C₅	1	1	yes	characteristic, complemented
168	#487	C₂²×C₅	1	1	yes	characteristic, complemented
169	#486	C₂²×C₅	1	1	yes	characteristic, complemented
170	#481	—	2	1	no	—
171	#480	—	2	1	no	—
172	#476	C₂²×C₅	1	2	yes	—
173	#474	C₂²×C₅	1	2	yes	—
174	#463	—	2	2	no	—
175	#459	C₂²×C₅	1	2	yes	—
176	#459	C₂²×C₅	1	2	yes	—
177	#449	—	2	2	no	—
178	#447	—	2	1	no	—
179	#447	—	2	1	no	—
180	#442	—	2	2	no	—
181	C₄×D₈	—	2	2	no	—
182	#436	—	2	2	no	—
183	#436	C₂²×C₅	1	2	yes	—
184	#436	C₂²×C₅	1	2	yes	—
185	#432	C₂²×C₅	1	1	yes	characteristic
186	#431	C₂²×C₅	1	1	yes	characteristic
187	#431	C₂²×C₅	1	1	yes	characteristic
188	#431	C₂²×C₅	1	1	yes	characteristic
189	#407	—	2	2	no	—
190	#335	C₂²×C₅	1	2	yes	complemented
191	#334	C₂²×C₅	1	2	yes	complemented
192	#333	C₂²×C₅	1	2	yes	complemented
193	#332	C₂²×C₅	1	2	yes	complemented
194	#331	C₂²×C₅	1	2	yes	complemented
195	#331	C₂²×C₅	1	2	yes	complemented
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	—	4	2	no	—
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	—	4	1	no	—
200	C₂³×C₅	—	8	1	no	—
201	C₂³×C₅	—	8	1	no	—
202	C₂³×C₅	#121	1	1	yes	characteristic
203	C₅×Q₈	—	4	2	no	—
204	C₅×Q₈	—	8	1	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	—	2	2	no	—
207	C₅×D₄	—	4	2	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	4	2	no	—
210	C₅×D₄	—	4	2	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	8	1	no	—
213	C₅×D₄	—	8	1	no	—
214	C₅×D₄	—	8	2	no	—
215	C₅×D₄	—	8	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	8	2	no	—
225	C₂×C₄×C₅	—	8	2	no	—
226	C₂×C₄×C₅	—	8	2	no	—
227	C₂×C₄×C₅	—	8	1	no	—
228	C₂×C₄×C₅	#121	1	1	yes	characteristic
229	C₂×C₄×C₅	#121	1	1	yes	characteristic
230	C₂×C₄×C₅	#121	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	4	2	no	—
237	C₅×C₈	—	4	2	no	—
238	C₅×C₈	—	4	2	no	—
239	C₂×#41	—	2	1	no	—
240	C₂×#41	—	2	1	no	—
241	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×D₈	—	2	2	no	—
245	C₂×D₈	—	2	2	no	—
246	C₂×D₈	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
250	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
251	#127	C₂³×C₅	1	1	yes	characteristic
252	#127	C₂³×C₅	1	1	yes	characteristic
253	#124	—	2	1	no	—
254	#124	—	2	1	no	—
255	#121	—	2	1	no	—
256	#121	—	2	1	no	—
257	#121	—	2	1	no	—
258	#121	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	C₅×D₄	1	2	yes	—
266	C₄×D₄	C₂³×C₅	1	2	yes	—
267	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
270	#107	—	2	2	no	—
271	#106	—	2	2	no	—
272	C₄⋊C₈	C₅×D₄	1	2	yes	—
273	C₄⋊C₈	C₂³×C₅	1	2	yes	—
274	C₄⋊C₈	C₂³×C₅	1	2	yes	—
275	C₄⋊C₈	C₂³×C₅	1	2	yes	—
276	#103	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	C₅×D₄	1	2	yes	—
288	#97	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	—	2	1	no	—
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	—	4	2	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	8	4	no	—
300	C₂²×C₅	—	8	1	no	—
301	C₂²×C₅	—	8	1	no	—
302	C₂²×C₅	—	8	1	no	—
303	C₂²×C₅	—	8	1	no	—
304	C₂²×C₅	—	8	1	no	—
305	C₂²×C₅	—	8	1	no	—
306	C₂²×C₅	C₂×#121	1	1	yes	characteristic
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	—	8	1	no	—
313	C₄×C₅	—	8	1	no	—
314	C₄×C₅	#575	1	2	yes	—
315	C₄×C₅	#576	1	2	yes	—
316	C₂⁴	—	2	1	no	—
317	#41	—	8	2	no	—
318	#41	—	8	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₅×#41	1	1	yes	characteristic
341	SD₁₆	—	8	2	no	—
342	D₈	—	4	4	no	—
343	D₈	—	4	4	no	—
344	D₈	—	8	2	no	—
345	M₁₆	—	8	2	no	—
346	M₁₆	—	8	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
351	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
365	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
366	C₄²	C₅×#41	1	1	yes	characteristic
367	C₄²	C₂⁴×C₅	1	1	yes	characteristic
368	C₂×C₅	—	4	1	no	—
369	C₂×C₅	—	8	2	no	—
370	C₂×C₅	—	16	1	no	—
371	C₂×C₅	—	16	1	no	—
372	C₂×C₅	#3041	1	1	yes	characteristic
373	C₂×C₅	#3054	1	1	yes	characteristic
374	C₂×C₅	#3068	1	1	yes	characteristic
375	C₂³	—	2	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	8	1	no	—
380	C₂³	—	8	1	no	—
381	C₂³	C₅×#121	1	1	yes	characteristic
382	Q₈	—	4	2	no	—
383	Q₈	—	8	1	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	1	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	C₅×#121	1	1	yes	characteristic
408	C₂×C₄	C₅×#121	1	1	yes	characteristic
409	C₂×C₄	C₅×#121	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₅	#19425	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	4	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	C₂×C₅×#121	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	C₅×#575	1	2	yes	—
441	C₄	C₅×#576	1	2	yes	—
442	C₂	—	4	1	no	—
443	C₂	—	8	2	no	—
444	C₂	—	16	1	no	—
445	C₂	—	16	1	no	—
446	C₂	C₅×#3041	1	1	yes	characteristic
447	C₂	C₅×#3054	1	1	yes	characteristic
448	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×#3207	C₂	semidirect
2. C₅×#3109	C₂	semidirect
3. C₅×#3100	C₂	semidirect
4. C₅×#2975	C₂	semidirect
5. C₅×#1703	C₂	semidirect
6. C₅×#1697	C₂	semidirect
7. C₅×#1687	C₂	semidirect
8. C₅×#1685	C₂	semidirect
9. C₅×#1572	C₂	semidirect
10. C₅×#1553	C₂	semidirect
11. C₅×#1543	C₂	semidirect
15. C₅×#493	C₂²	semidirect
16. C₅×#492	C₂²	semidirect
17. C₅×#487	C₂²	semidirect
18. C₅×#486	C₂²	semidirect
39. C₅×#335	C₂²	semidirect
40. C₅×#334	C₂²	semidirect
41. C₅×#333	C₂²	semidirect
42. C₅×#332	C₂²	semidirect
43. C₅×#331	C₂²	semidirect
44. C₅×#331	C₂²	semidirect
45. #19425	C₅	direct (N × H)
100. #3207	C₂×C₅	semidirect
101. #3109	C₂×C₅	semidirect
102. #3100	C₂×C₅	semidirect
103. #2975	C₂×C₅	semidirect
104. #1703	C₂×C₅	semidirect
105. #1697	C₂×C₅	semidirect
106. #1687	C₂×C₅	semidirect
107. #1685	C₂×C₅	semidirect
108. #1572	C₂×C₅	semidirect
109. #1553	C₂×C₅	semidirect
110. #1543	C₂×C₅	semidirect
166. #493	C₂²×C₅	semidirect
167. #492	C₂²×C₅	semidirect
168. #487	C₂²×C₅	semidirect
169. #486	C₂²×C₅	semidirect
190. #335	C₂²×C₅	semidirect
191. #334	C₂²×C₅	semidirect
192. #333	C₂²×C₅	semidirect
193. #332	C₂²×C₅	semidirect
194. #331	C₂²×C₅	semidirect
195. #331	C₂²×C₅	semidirect
418. C₅	#19425	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3207	2
C₅×#3109	2
C₅×#3100	2
C₅×#2975	2
C₅×#1703	2
C₅×#1697	2
C₅×#1687	2
C₅×#1685	2
C₅×#1572	2
C₅×#1553	2
C₅×#1543	2
#19425	5

Subgroups — C5×#19425 #11942145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19425 #11942145